Resources tagged with: Generalising

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Broad Topics > Thinking Mathematically > Generalising

Hidden Rectangles

Age 11 to 14
Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Jam

Age 14 to 16
Challenge Level

To avoid losing think of another very well known game where the patterns of play are similar.

Sliding Puzzle

Age 11 to 16
Challenge Level

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Window Frames

Age 5 to 14
Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Jam

Age 14 to 16
Challenge Level

A game for 2 players

Have You Got It?

Age 11 to 14
Challenge Level

Can you explain the strategy for winning this game with any target?

Card Trick 2

Age 11 to 14
Challenge Level

Can you explain how this card trick works?

Shear Magic

Age 11 to 14
Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Number Pyramids

Age 11 to 14
Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Christmas Chocolates

Age 11 to 14
Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Got It

Age 7 to 14
Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

One, Three, Five, Seven

Age 11 to 16
Challenge Level

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

Got it for Two

Age 7 to 14
Challenge Level

Got It game for an adult and child. How can you play so that you know you will always win?

Nim-7 for Two

Age 5 to 14
Challenge Level

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Pentanim

Age 7 to 16
Challenge Level

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

Partly Painted Cube

Age 14 to 16
Challenge Level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Cubes Within Cubes Revisited

Age 11 to 14
Challenge Level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Nim-7

Age 5 to 14
Challenge Level

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Egyptian Fractions

Age 11 to 14
Challenge Level

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Enclosing Squares

Age 11 to 14
Challenge Level

Can you find sets of sloping lines that enclose a square?

Train Spotters' Paradise

Age 11 to 16

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

Consecutive Negative Numbers

Age 11 to 14
Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Partitioning Revisited

Age 11 to 14
Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Keep it Simple

Age 11 to 14
Challenge Level

Can all unit fractions be written as the sum of two unit fractions?

Cuboid Challenge

Age 11 to 16
Challenge Level

What's the largest volume of box you can make from a square of paper?

Picturing Square Numbers

Age 11 to 14
Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Painted Cube

Age 14 to 16
Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Frogs

Age 11 to 14
Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Konigsberg Plus

Age 11 to 14
Challenge Level

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Nim

Age 14 to 16
Challenge Level

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

Nim-like Games

Age 7 to 16
Challenge Level

A collection of games on the NIM theme

More Twisting and Turning

Age 11 to 16
Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes...

Arithmagons

Age 11 to 16
Challenge Level

Can you find the values at the vertices when you know the values on the edges?

More Number Pyramids

Age 11 to 14
Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Hypotenuse Lattice Points

Age 14 to 16
Challenge Level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

Multiplication Arithmagons

Age 14 to 16
Challenge Level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Building Gnomons

Age 14 to 16
Challenge Level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

More Magic Potting Sheds

Age 11 to 14
Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Thank Your Lucky Stars

Age 14 to 16
Challenge Level

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

Steel Cables

Age 14 to 16
Challenge Level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Squares in Rectangles

Age 11 to 14
Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Magic Letters

Age 11 to 14
Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

One O Five

Age 11 to 14
Challenge Level

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

A Tilted Square

Age 14 to 16
Challenge Level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Is There a Theorem?

Age 11 to 14
Challenge Level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Cunning Card Trick

Age 11 to 14
Challenge Level

Delight your friends with this cunning trick! Can you explain how it works?